{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:4O4U4CL3D5TDC6IC5YGH7HP6H6","short_pith_number":"pith:4O4U4CL3","canonical_record":{"source":{"id":"2404.04091","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-04-05T13:31:51Z","cross_cats_sorted":[],"title_canon_sha256":"b91f23d1c843ff8de595d49b013e59f4dd13f9cfd9909bc7b40276997d2aa858","abstract_canon_sha256":"4fc187a7cdfade42e5618553017ecff41039f34c4329519cc56096fcf4ecf460"},"schema_version":"1.0"},"canonical_sha256":"e3b94e097b1f66317902ee0c7f9dfe3fb8032260f9a964fbada9720f2b256f27","source":{"kind":"arxiv","id":"2404.04091","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.04091","created_at":"2026-07-05T08:04:45Z"},{"alias_kind":"arxiv_version","alias_value":"2404.04091v1","created_at":"2026-07-05T08:04:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.04091","created_at":"2026-07-05T08:04:45Z"},{"alias_kind":"pith_short_12","alias_value":"4O4U4CL3D5TD","created_at":"2026-07-05T08:04:45Z"},{"alias_kind":"pith_short_16","alias_value":"4O4U4CL3D5TDC6IC","created_at":"2026-07-05T08:04:45Z"},{"alias_kind":"pith_short_8","alias_value":"4O4U4CL3","created_at":"2026-07-05T08:04:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:4O4U4CL3D5TDC6IC5YGH7HP6H6","target":"record","payload":{"canonical_record":{"source":{"id":"2404.04091","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-04-05T13:31:51Z","cross_cats_sorted":[],"title_canon_sha256":"b91f23d1c843ff8de595d49b013e59f4dd13f9cfd9909bc7b40276997d2aa858","abstract_canon_sha256":"4fc187a7cdfade42e5618553017ecff41039f34c4329519cc56096fcf4ecf460"},"schema_version":"1.0"},"canonical_sha256":"e3b94e097b1f66317902ee0c7f9dfe3fb8032260f9a964fbada9720f2b256f27","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:04:45.335523Z","signature_b64":"8fZUMa9F/L8e1xhOjFnUpbbXRGHSDJOePsgdFaPsDn9AH/GooMxXpQjD3BQt/hSZb8WWprC7v6mIuoCHPZhMAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e3b94e097b1f66317902ee0c7f9dfe3fb8032260f9a964fbada9720f2b256f27","last_reissued_at":"2026-07-05T08:04:45.335120Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:04:45.335120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2404.04091","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:04:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W5y99Y2TTXVYLcZI+RaGp3ty4EoTLp/UdKfRe3xNbhaKfP1xSd76aaZ5euBV/O1Ce5kqO/tPc3KzDFdfSGUiDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T20:33:36.422085Z"},"content_sha256":"a7e2d5cd0bb2fd6be8e5156ce19dfa1b5e6758e068ec8294cb52447354bf9fe6","schema_version":"1.0","event_id":"sha256:a7e2d5cd0bb2fd6be8e5156ce19dfa1b5e6758e068ec8294cb52447354bf9fe6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:4O4U4CL3D5TDC6IC5YGH7HP6H6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bijections on pattern avoiding inversion sequences and related objects","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Heesung Shin, JiSun Huh, Sangwook Kim, Seunghyun Seo","submitted_at":"2024-04-05T13:31:51Z","abstract_excerpt":"The number of inversion sequences avoiding two patterns $101$ and $102$ is known to be the same as the number of permutations avoiding three patterns $2341$, $2431$, and $3241$. This sequence also counts the number of Schr\\\"{o}der paths without triple descents, restricted bicolored Dyck paths, $(101,021)$-avoiding inversion sequences, and weighted ordered trees. We provide bijections to integrate them together by introducing $F$-paths. Moreover, we define three kinds of statistics for each of the objects and count the number of each object with respect to these statistics. We also discuss dire"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.04091","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2404.04091/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:04:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"itNHfrWYmjANcsETrKJwNy2Brok96s6v+o9C+kJP9jh4jvkA/DlGTSD0t7Ml9OIyKXupuYC1LRfZwXM0VTTdAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T20:33:36.423073Z"},"content_sha256":"d2a4c276bc132b4a357723c6a43ffba348e2b648a2635f024c9add068082e91f","schema_version":"1.0","event_id":"sha256:d2a4c276bc132b4a357723c6a43ffba348e2b648a2635f024c9add068082e91f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4O4U4CL3D5TDC6IC5YGH7HP6H6/bundle.json","state_url":"https://pith.science/pith/4O4U4CL3D5TDC6IC5YGH7HP6H6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4O4U4CL3D5TDC6IC5YGH7HP6H6/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-17T20:33:36Z","links":{"resolver":"https://pith.science/pith/4O4U4CL3D5TDC6IC5YGH7HP6H6","bundle":"https://pith.science/pith/4O4U4CL3D5TDC6IC5YGH7HP6H6/bundle.json","state":"https://pith.science/pith/4O4U4CL3D5TDC6IC5YGH7HP6H6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4O4U4CL3D5TDC6IC5YGH7HP6H6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:4O4U4CL3D5TDC6IC5YGH7HP6H6","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"4fc187a7cdfade42e5618553017ecff41039f34c4329519cc56096fcf4ecf460","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-04-05T13:31:51Z","title_canon_sha256":"b91f23d1c843ff8de595d49b013e59f4dd13f9cfd9909bc7b40276997d2aa858"},"schema_version":"1.0","source":{"id":"2404.04091","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.04091","created_at":"2026-07-05T08:04:45Z"},{"alias_kind":"arxiv_version","alias_value":"2404.04091v1","created_at":"2026-07-05T08:04:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.04091","created_at":"2026-07-05T08:04:45Z"},{"alias_kind":"pith_short_12","alias_value":"4O4U4CL3D5TD","created_at":"2026-07-05T08:04:45Z"},{"alias_kind":"pith_short_16","alias_value":"4O4U4CL3D5TDC6IC","created_at":"2026-07-05T08:04:45Z"},{"alias_kind":"pith_short_8","alias_value":"4O4U4CL3","created_at":"2026-07-05T08:04:45Z"}],"graph_snapshots":[{"event_id":"sha256:d2a4c276bc132b4a357723c6a43ffba348e2b648a2635f024c9add068082e91f","target":"graph","created_at":"2026-07-05T08:04:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2404.04091/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The number of inversion sequences avoiding two patterns $101$ and $102$ is known to be the same as the number of permutations avoiding three patterns $2341$, $2431$, and $3241$. This sequence also counts the number of Schr\\\"{o}der paths without triple descents, restricted bicolored Dyck paths, $(101,021)$-avoiding inversion sequences, and weighted ordered trees. We provide bijections to integrate them together by introducing $F$-paths. Moreover, we define three kinds of statistics for each of the objects and count the number of each object with respect to these statistics. We also discuss dire","authors_text":"Heesung Shin, JiSun Huh, Sangwook Kim, Seunghyun Seo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-04-05T13:31:51Z","title":"Bijections on pattern avoiding inversion sequences and related objects"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.04091","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:a7e2d5cd0bb2fd6be8e5156ce19dfa1b5e6758e068ec8294cb52447354bf9fe6","target":"record","created_at":"2026-07-05T08:04:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"4fc187a7cdfade42e5618553017ecff41039f34c4329519cc56096fcf4ecf460","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-04-05T13:31:51Z","title_canon_sha256":"b91f23d1c843ff8de595d49b013e59f4dd13f9cfd9909bc7b40276997d2aa858"},"schema_version":"1.0","source":{"id":"2404.04091","kind":"arxiv","version":1}},"canonical_sha256":"e3b94e097b1f66317902ee0c7f9dfe3fb8032260f9a964fbada9720f2b256f27","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e3b94e097b1f66317902ee0c7f9dfe3fb8032260f9a964fbada9720f2b256f27","first_computed_at":"2026-07-05T08:04:45.335120Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:04:45.335120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8fZUMa9F/L8e1xhOjFnUpbbXRGHSDJOePsgdFaPsDn9AH/GooMxXpQjD3BQt/hSZb8WWprC7v6mIuoCHPZhMAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:04:45.335523Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.04091","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a7e2d5cd0bb2fd6be8e5156ce19dfa1b5e6758e068ec8294cb52447354bf9fe6","sha256:d2a4c276bc132b4a357723c6a43ffba348e2b648a2635f024c9add068082e91f"],"state_sha256":"77e0483bc83e2a885851cee8afbf92459698af2d4217dd53679433fef4e6bf96"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Kvi3GctPTeBTPoTrrjHv+hvxiHXA95Cn1FUClS60OsP0AGxCobkEEhK+xPYBNgv7Hgdqz/l0nAuQCWbkcGEXCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T20:33:36.430522Z","bundle_sha256":"7dcac078a080b8ede35b64b65649b0f54bc83cb2eed1def501d853221fdd382d"}}